Domanda del libro di testo
A particle moving on the x-axis experiences a force given by Fx = qx², where q is a constant. How much work is done on the particle as it moves from x = 0 to x = d?
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Ch 09: Work and Kinetic Energy
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
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Capitolo 9, Problema 26
A horizontal spring with spring constant 750 N/m is attached to a wall. An athlete presses against the free end of the spring, compressing it 5.0 cm. How hard is the athlete pushing?
Guida verificata passo dopo passo1
Step 1: Identify the formula for the force exerted by a spring, which is given by Hooke's Law: , where is the force, is the spring constant, and is the displacement of the spring from its equilibrium position.
Step 2: Convert the displacement from centimeters to meters, as SI units are required for calculations. Since 1 cm = 0.01 m, the displacement is .
Step 3: Substitute the given values into Hooke's Law. The spring constant is , and the displacement is . The formula becomes: .
Step 4: Perform the multiplication to find the force. Multiply the spring constant by the displacement . This will give the magnitude of the force exerted by the spring.
Step 5: Interpret the result. The force calculated represents how hard the athlete is pushing against the spring to compress it by 5.0 cm. Ensure the units of the final answer are in Newtons (N), as force is measured in Newtons in the SI system.
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Hooke's Law
Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position, provided the elastic limit is not exceeded. Mathematically, it is expressed as F = -kx, where F is the force, k is the spring constant, and x is the displacement. This principle is essential for understanding how the spring responds to compression or extension.
Video consigliato:
Percorso guidato
05:27
Spring Force (Hooke's Law)
Spring Constant
The spring constant, denoted as k, is a measure of a spring's stiffness. It is defined as the force required to compress or extend the spring by a unit distance. A higher spring constant indicates a stiffer spring that requires more force to compress or stretch, which is crucial for calculating the force exerted by the athlete in this scenario.
Video consigliato:
Percorso guidato
08:59Phase Constant of a Wave Function
Force Calculation
To determine how hard the athlete is pushing against the spring, one must calculate the force using Hooke's Law. By substituting the values of the spring constant and the displacement into the formula F = kx, where k is 750 N/m and x is 0.05 m (5.0 cm), we can find the force exerted by the athlete, which directly correlates to the compression of the spring.
Video consigliato:
Percorso guidato
06:09Work Done by a Constant Force
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A 35-cm-long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. What is the spring constant?
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Domanda del libro di testo
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Domanda del libro di testo
A horizontal spring with spring constant 85 N/m extends outward from a wall just above floor level. A 1.5 kg box sliding across a frictionless floor hits the end of the spring and compresses it 6.5 cm before the spring expands and shoots the box back out. How fast was the box going when it hit the spring?
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Domanda del libro di testo
A 5.0 kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in FIGURE EX9.28. The scale reads in newtons. The scale reads 20 N when the lower spring has been compressed by 2.0 cm. What is the value of the spring constant for the lower spring?
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Domanda del libro di testo
A 2.0 kg particle moving along the x-axis experiences the force shown in FIGURE EX9.22. The particle's velocity is 3.0 m/s at x = 0 m. At what point on the x-axis does the particle have a turning point?
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